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sergiy2304 [10]
3 years ago
15

Given ABE is an isosceles triangle with ZABE - 100° and AMNP is an isosceles triangle with one base angle measuring 40°. Are

Mathematics
1 answer:
MrMuchimi3 years ago
8 0

Two triangle ABE and MNP are similar by AA criterion

Step-by-step explanation:

Given that ABE is an isosceles Δ with ABE= 100°

this means that some of the other two angles must be =180°-100°=80°

Since the triangle is an isosceles Δ meaning two sides measure must be equal, it means the other two sides measure 40° each.

∠BAC=∠ACB=40°

In MNP one of the base angles is 40° and the triangle is isosceles. For an  isosceles triangle base angles are always equal hence other base angle is also 40° meaning

the angle measures come out to be 40°,40° and 100°

Since all the angle measures are same the two triangles are similar in aspect by AA criterion where AA refers to "angle-angle"

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A game involves one flip of a penny and one spin of a spinner with 3 sections numbered 1, 2, and 3. Which of the following could
siniylev [52]

Answer: 1

Step-by-step explanation:

5 0
3 years ago
Barbara made a bad investment. Rather than earning interest, her money is decreasing in value by 11% each week! After just one w
pochemuha

Answer: She started with $160.

It will take 6 weeks before she has less than half of what she originally invested.

Step-by-step explanation:

If her money is decreasing in value by 11% each week, it means that the rate at which it is decreasing is exponential.

We would apply the formula for exponential decay which is expressed as

A = P(1 - r)^t

Where

A represents the value of the investment after t weeks.

t represents the number of weeks.

P represents the initial value of the investment.

r represents rate of depreciation.

From the information given,

A = $142.40

r = 11% = 11/100 = 0.11

t = 1

Therefore

142.40 = P(1 - 0.11)^1

142.40 = P(0.89)

P = 142.4/0.89

P = 160

For her to have half of what she invested originally, then

80 = 160(0.89)^t

80/160 = (0.89)^t

0.5 = (0.89)^t

Taking log of both sides to base 10

Log 0.5 = log0.89^t = tlog0.89

- 0.3010 = - 0.051t

t = - 0.3010/- 0.051

t = 5.9

Approximately 6 weeks

5 0
3 years ago
How many learners can enrol if there are 12 teachers and a ratio of teachers to learners is 30:1
VladimirAG [237]

Answer:

360 learners

Step-by-step explanation:

One way to solve these types of problems is that you could set up a proportion

learners/teachers = learners/teachers

Let x = no. of learners to enrol

30/1 = x/12

12(30) = x

x = 360 learners

5 0
3 years ago
For the class of 2013's prom Norman's dress shop sold cheaper dresses for $90 each and more expensive dresses for $140 each. The
Tema [17]

Answer:

Number of cheaper dresses sold  is 35

Number of expensive  dresses sold  is 15

Step-by-step explanation:

Given:

Cost of cheaper dresses = $90

Cost of  expensive dresses = $140

Total cost of  the dresses = $5250

To Find:

Number of cheaper dress = ?

Number of expensive  dress = ?

Solution:

Let

The number of  cheaper dresses be x

The number of  expensive dresses be y

(Number of cheaper dresses X cost of cheap dress) +  (Number of Expensive dresses X cost of  expensive dress)  =  $5250

x \times90 +y \times 140 = 5250=  $5250

It is given that the 20 more of the cheaper dresses than the expensive dresses is sold

So,

number of cheaper dress  =  20  +  number of expensive dress

x = 20 + y---------------------------------------(1)

(20+y) \times90 +y \times 140 = 5250 = 5250

(20 \times 90 +y\times 90) +y \times 140= 5250

1800 + 90y+ 140y = 5250

1800 + 230y = 5250

230y =5250 -1800

230y = 3450

y = \frac{3450}{230}

y = 15

Substituting y in (1)

x = 20 +15

x= 35

5 0
3 years ago
Can you simplify the square root of -8
lapo4ka [179]

Answer:

I don't think so.

Step-by-step explanation:

But what do I know? XD

3 0
3 years ago
Read 2 more answers
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